Inverse tangent based switching type reaching law for discrete time sliding mode control systems

In this work the reaching law approach to the sliding mode control of discrete time systems is considered. We propose a reaching law, in which the convergence of the sliding variable to the vicinity of zero is governed by the inverse tangent function. First we analyze the case of the unperturbed system, and then we consider a second scenario with unknown disturbances and parameter uncertainties. We demonstrate, that for both cases the presented reaching law guarantees the quasi sliding motion of the representative point defined as crossing the sliding hyperplane in each successive control period while remaining inside an a priori known band around the hyperplane. When compared to the most popular, constant plus proportional reaching law, the proposed solution offers better robustness and faster convergence.